Despite efforts made by teachers and researchers, studies show that digital technologies have not improved conditions for teaching and learning mathematics to the degree expected by stakeholders inside as well as outside the school system.

In this research, the problem of the integration of digital technologies is addressed through the perspective of design. It sets out to explore the conditions where educational design researchers may succeed in producing valuable and sustainable contributions to teacher change. The design approach developed and used for this purpose is Agile Educational Design (AED). It shares many of the common features of other design methodologies within the field; however, the AED approach is an explicit systems approach to design based on the Singerian philosophy of design. Rather than focus on ready-made products or other resources such as curriculum material, professional development or design principles, the focus is on processes and supporting teachers’ operationalisation of theoretical principles to achieve change. It is argued that all phases of the design process need to be considered from a research perspective. The developmental phases cannot be treated as uncomplicated inputs that only serve as a ‘design base’ for research activities. The Anthropological Theory of the Didactic is used as an overall theoretical framework to describe all aspects of the design process and to analyse the empirical data which consists of three design cycles related to three different ways of interacting with teachers. The design cycles were carried out in various settings, including different schools (secondary level) and with different teachers and different learning objectives. The dynamic geometry software GeoGebra was used in all three cycles.

The results highlight some of the internal and external constraints that hinder teachers from integrating digital technologies in an effective way to support students learning mathematics. Digital technologies introduce important epistemological changes in the mathematical content that may explain some of the teachers’ difficulties in exploiting the full potential of digital technologies. However, giving teachers the responsibility for orchestrating lessons in accordance with theoretical principles provided by a researcher showed promising results regarding achieving sustainable changes in teachers’ practices.

In this paper, the notion of adaptive conceptual frameworks is presented. These frameworks have been used to conduct educational design research aiming at developing ICT supported mathematics instruction. In this approach, empirical data is connected with various theories in an adaptive and iterative process. Differentiation is made between conceptual framework for development (CFD) and conceptual framework for understanding (CFU) depending on how the frameworks are used in the design process. The use of adaptive conceptual frameworks contributes to the transparency in the design process by making explicit the levels at which different theories operate and how the design process is evaluated.

In this paper, we present preliminary results related to a developmental project where we explore how technology can be used to improve teachers’ teaching practices and their students’ learning of mathematics. We have adopted a teacher-centered, collaborative approach that challenges the participating researcher to develop strategies for finding different forms of scaffolding to support the teachers’ participation in this project. So far, we have used the software GeoGebra to provide competence development for the teachers in terms of mathematical representations. This software will also have a central role when investigating how the teachers perceive and make use of different affordances provided by technologies when addressing a specific learning goal related to the teaching of algebra at a lower secondary school.

Supporting teachers’ instrumental genesis2015In: Mathematics and Science: The relationships and disconnections between researchand education: Papers from a doctoral course at the University of Copenhagen / [ed] Marianne Achiam, Carl Winsløw, Copenhagen: Department of Science Education, University of Copenhagen , 2015, p. 93-105Chapter in book (Other academic)

Abstract [en]

In this paper we unpack some of the critical issues whensupporting teachers in the appropriate and effective use of the affordances provided by ICT in mathematics classrooms. Our findings suggest that the integration of ICT may need to be accompaniedby resources that could aid the teacher in the process of transformingICT into effective instruments for teaching and learning.

6.

Perez, Miguel

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

In this paper, the validity of “theoretical seeding” to support the transformation of mathematics teaching is studied in a case of professional development related to the design of learning activities supported by information and communication technologies (ICT). Theoretical seeding includes the use of a theoretical construct and teachers as agents of change of practice. The results suggest that the validity of theoretical seeding, with regard to the social consequences, is tentatively sufficient to consider it as purposeful and appropriate. Furthermore, the effects of theoretical seeding show a promising potential for future design efforts in terms of achieving theoretically underpinned and sustainable changes in teachers’ practices with ICT.

In this paper we present some preliminary findings from an ongoing research project with the aim of developing mathematics instruction supported by ICT at secondary school level. Focusing on the affordances for communication provided by ICT, these findings suggest that a successful integration of ICT to support the learning of mathematics may require behavioral change on the part of teachers.